T shaped drain on bathroom sink?

I am pretty new to this stuff but I have unclogged a couple P drains in my time. I am attempting to replace my bathroom sink but I couldn't find a pipe fitting at Home Depot that looks like the following :

Yep I went to a more informed plumbing supply only place that knew more than home depot, showed them my disassembled plumbing and the guy immediately identified it as AC overflow, and helped me find it. Home depot and lowes didn't seem to have the 5/8" size that I needed. I'm going back to the new place when I get to replacing my second sink and a couple of other odds and ends, they really seem to know what they're talking about.

The picture is huge and limited in scope, but they make a chrome branch tee that screws into the sink fitting, and replaces the metal part above your tee fitting, IF the hose is high enough in the wall to drain into it. The hose is usually 3/4" i.d.

I figured it out after MACPLUMB777 said "A/C overflow" I went to a plumbing supply house and they knew exactly what I needed unlike the Home Depot people who said they'd never seen anything like that and I'm pretty sure they didn't have it either, I went through the whole 1 1/2" PVC section multiple times. And yeah I saw both 3/4" and 5/8" sizes for the tee. It's all together now and working just fine. Thanks for the responses.